Recent empirical research finds that pairs of countries with stronger trade linkages tend to have more highly correlated business cycles. We assess whether the standard international business cycle framework can replicate this intuitive result. We employ a three-country model with transportation costs. We simulate the effects of increased goods market integration under two asset market structures: complete markets and international financial autarky. Our main finding is that under international financial autarky the model can generate stronger correlations for pairs of countries that trade more, but the increased correlation falls far short of the empirical findings. In our benchmark calibrations, the model explains at most 6 percent of the responsiveness of GDP correlations to trade found in the empirical research. This result is robust to many combinations of shock specifications, import shares, and elasticities of substitution. Because the difference between business cycle theory and the empirical results cannot be resolved by changes in parameter values and the structure of the standard models, we call this discrepancy the trade comovement problem.